b. The parametric equation of a surface S is given by r(u,v) = [2vcos u , vsin u , v], 2

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
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i need to solve question (b) part ii

a. Using Green's Theorem in plane , find the area of the region enclosed by the curve
whose parametric equation is r() = [3 cos t,2 sin t], 0 < t< 2n .
b. The parametric equation of a surface S is given by
r(u, v)
= [2 vcos u, vsin u , v], susn, 0< v< 1
2
i. Find the Cartesian equation of the surface S, then identify this surface.
ii. Evaluate the surface integral ||F.ndA, where F(x, y, z) = [e?y ,1, sin(rz)].
Transcribed Image Text:a. Using Green's Theorem in plane , find the area of the region enclosed by the curve whose parametric equation is r() = [3 cos t,2 sin t], 0 < t< 2n . b. The parametric equation of a surface S is given by r(u, v) = [2 vcos u, vsin u , v], susn, 0< v< 1 2 i. Find the Cartesian equation of the surface S, then identify this surface. ii. Evaluate the surface integral ||F.ndA, where F(x, y, z) = [e?y ,1, sin(rz)].
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